Qm Definition and 1000 Threads

Homework Statement Here's something that's confusing me. Say we have a potential V(x) = Vo if x < 0, x > a and V(x) = 0 if 0 < x < a (yes I know the notation with greater than/equals etc isn't totally correct, but you know what I'm talking about.) In the middle section, ψ'' +...

Hello, my question is a simple one: I am attempting to do problem 2.31 in Griffiths' QM book (latest edition). The question states, "The Dirac Delta function can be thought of as the limiting case of a rectangle of area 1, as the height goes to infinity and the width to zero. Show that the...

I need the math. I get a little bored doing the low level stuff, and want to jump into it. As long as I'm interested I won't get bored. I started the other thread discrete wave functions below, and realized I like everything about QM. Hopefully I don't get bored. Sorry I just read the forum...

Hi, The violation of Bell's inequality says that quantum mechanics can't be both local and realistic. Let's assume it is realistic but non-local. How does this explain the fact that a single particle can be in a superposition that collapses to a particular state when measured? Since we only...

Hello all! On the problem of taking elements of different (degenerated-)state vectors that do not vanish on the perturbation matrix, Weinberg uses the following approach, when dealing with the Zeeman effect: In this way, he goes from the first to the second equation shown as attachments...

Does anyone know good notes or a book on quantum mechanics that covers well the interpretational issues? Especially, which deals also with the last fifty or sixty years, i.e. that has Bell, decoherence, GHZ, Aspect experiment, Mach-Zehnder interferometer, delayed-choice, mesocopic Schrödinger...

Does QM hint at time-space being an emergent, rather than a fundamental, property/constituent of nature? In what ways? Electromagnetic (EM) fields are assumed to pervade all of time-space. Which is more fundamental?

i need help -- what are prerequisites for studying QM? i have always had an interest in different fields of science, but lately i have become extremely interested in quantum mechanics. i know that there may be different subdivisions of the field, but I'm more interested in like theoretical...

It seems the most advanced physics engineers are using is basic quantum mechanics. Is it accurate to say this is the "final frontier" of engineering? The field of particle physics, for example, has been established for nearly 50 years now and there are still no practical uses of the incredible...

"The" Classical Path, QM Path Integrals and Paths in Curved Spacetime Hey Guys! I've got an exciting question! It's been burning on my mind for years, but I think I can formulate it now. It's not so much a specific question, but rather a physical story which perhaps this thread can uncover...

Are there any modern interpretations of QM that predict the correlations in a Bell Inequality violation ? Preferably a local non realistic model based on mechanisms.

Before measurements, quantum states are vectors in Hilbert space and there may not even be momentum or position chosen before wave function collapse or measurement. I'd like to understand how mass or the higgs field couple to wave function. Can higgs home into the specific ray or vector in...

Hello I read the follow paper about van del waals interaction in quantum mechanics http://www.damtp.cam.ac.uk/user/gold/pdfs/teaching/van_der_waals.pdf In this paper the potential V= e^2/R + e^2/(R+y)+e^2/(R-x)+ e^2/(R+y-x) is aproximated to V \approx -2 e^2/R^3 xy with R>>|x|,|y| why...

Hi all, I'm having conceptual troubles understanding the significance of the potential energy term in Schrodinger's equation. More specifically, the physical meaning of the potential "wells" is not clicking with me; my textbook is not making this very clear. For clarity, consider an...

Hi, material on learning the calculus way are plentiful but I can't find anywhere to teach me the matrix way, any links? I can't even find out how to represent the Hamiltonian as a matrix. Thanks in advance

Homework Statement sup guys! I think I've solved this set of problems, but I was just wondering if I've done it right - I have no way to tell. I'll put all the questions and answers here - plus the stuff I used. So could you please tell me if there's any mistakes? Here it is - using Word...

What are some open problems in the interplay between Quantum Mechanics and the 2nd Law of Thermodynamics? thanks

Homework Statement Hey everyone! The question is this: Consider a two-state system with normalized energy eigenstates \psi_{1}(x) and \psi_{2}(x), and corresponding energy eigenvalues E_{1} and E_{2} = E_{1}+\Delta E; \Delta E>0 (a) There is another linear operator \hat{S} that acts by...

Homework Statement A number of spin 1/2 particles are run through a Stern-Gerlach apparatus and when the emerge they all have the same spin wave function (ψ1, ψ2)τ and 9/25 are in the +z direction and 16/25 are in the -z direction with the normal basis column vectors for +z and -z...

Hi, I'm studying http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison_of_interpretations but have trouble with the apparent differences of the key concepts: * deterministic - unique history * wavefunction real - hidden variables - counterfactual definiteness I...

Homework Statement Consider a one-dimensional quantum system described by the potential: $$V(x) = -V_o + \frac{1}{2}mw^2x^2\,\,,V_o > 0\,\,\text{for}\,\, |x| < b\,\,\text{and}\,\,0\,\,\text{otherwise}$$ Show that the state described by: $$\psi_{-}(x) = R_{-}...

Trying to relate a bit better to where QM stops, and Interpretations begin. Especially with respect to Decoherence. Is Decoherence seen as a measurable phenomena, or, just as a "possible" explanation for measurable phenomena? Obviously when I mark a path in a 2 slit experiment I cause...

I've been wrestling with this question for a while and can't seem to find anything in my notes that will help me. Homework Statement Determine whether the wave function \Psi (x,t)= \textrm{exp}(-i(kx+\omega t)) is an eigenfunction of the operators for total energy and x component of momentum...

My first of many GR questions :cool:: If electromagnetism can be incorporated into the standard model, where I think of electromagnetism as derivable from an action principle ala Landau-Lifshitz, at what point does this process stop working when you use gravitation? I was thinking the...

This is a quantum mechanics problem, but the problem itself is reduced (naturally) to a differential equations problem. I have to solve the following equation: \frac{\partial}{\partial t}\psi (x,t) = i\sigma \psi (x,t) where \sigma > 0 The initial condition is: \psi (x,0) =...

Homework Statement Hi The density matrix evolves as \dot \rho = -\frac{i}{\hbar}[H,\rho] but is this equation written in the Schrödinger or Heisenberg picture? I'm not entirely sure how to figure this out. In my book it just mentions the equation, not how it is derived (which may have given...

I recently read an article (http://vixra.org/abs/1308.0143) written by an acquaintance, Dr Dimitar Valev and wanted opinions on its relevance . Basically, dimensionless ratios are derived from equations based on both the Planck constant and the Hubble constant. Thus, Quantum Mechanics and...

Hi everyone, I'm currently working my way through Dirac's Quantum Mechanics, and I found this proof really irritating. We're trying to demonstrate that any eigenket can be expressed as a sum of eigenkets of a real linear function \xi which satisfies the equation \varphi(\xi) =...

Hi guys, The other day I was struggling to to grasp some of the concepts in QM. I realized I would never understand without understanding the math. From what I know the following book is what they give to first year university students. I'm on page 20, and I am struggling. But I'm determined to...

Homework Statement A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations The following equation for the transmission coefficient, T, is given: T = [1 + \frac{V_0 ^2...

I'm pretty sure a proton's location does not have much quantum uncertainty but an up quark does. So qm uncertainty begins around 10^-15m and is full blown at 10^-18m If my numbers are wrong please let me know.

I have read a lot of stuff on Quantum Mechanics and there seem to be a lot of outlandish theories on the web mixing QM with every religion in a search for god as the great observer. I would really love to get my hands on a good college level textbook that explains the more supported theories...

According to Griffiths QM book, after he derived the stationary state solutions to the Schrodinger equation for a particle in an infinite potential well, which are just functions of sine, he claims that these stationary solutions are orthogonal and complete. I agree that they are orthogonal...

I'm seeing lots of underlying connections between the canonical formulism of QFT and QM. But I'm getting a bit confused by their differences. I'll just write down my thought process: QM is a one parameter system (t) in a space with three quantized operators (x,y,z) QFT is a four parameter...

What is the best intro to QM? I was settled on Griffiths, but it seems there are only two kinds of people in this world, those who recommenced Griffiths, and those who strongly don't recommended it. I'll give a bit of background, so I can get the best possible recommendations. I'm...

I am in a philosophy club where we meet to discuss a topic each month. Next month I have undertaken to kick off a discussion on the philosophical implications of quantum mechanics. I expect interpretations of QM, especially things like MWI, to be a significant part of that. I need to find...

Homework Statement A parallel beam of neutrons with speed 200m/s is incident on an absorbing sheet with a slit of width 0.01mm. Calculate the width of the beam 10m behind the slit. Hint The slit localizes the neutrons transversely (y) to their propagation direction x. The resulting ΔPy gives...

i get that the Waves represent the probability density of the object, but a wave has a crest and a trough. What does the specifically does the trough represent? what specifically does the crest represent?

Let's say we have a one dimensional single particle system that is described by a SE -\frac{\hbar^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi(x)+V(x)\psi(x)=E\psi(x) We do not know what the potential energy function V(x) is, but we know that the eigenvalues spectrum is E_{n}=kn^{\frac{3}{2}}...

Just want to clarify my understanding of these things. Fermions obey the Pauli Exclusion Principal, meaning meaning only one particle can occupy a single state. This means the wave function is anti-symmetric under particle exchange. That's the part that isn't making much sense. Is it because...

Homework Statement Given the operators \hat{x}=x\cdot and \hat{p}=-i\hbar \frac{d}{dx}, prove that: [\hat{x}, g(\hat{p})]=i\hbar \frac{dg}{d\hat p}Homework Equations None. The Attempt at a Solution I have very little idea on how to begin this problem, but I don't want a solution, I simply...

Hello, I am working my way though Sakurai's book on Quantum MEchanics and am having some problems understanding the bra-ket notation. I keep believing I understand everything there is to it but then he will do something in a single line that I cannot understand. This is one of them. If...

Decades of work are being put in trying to find a unified theory which can accommodate both General Relativity and the Standard Model. I guess that the attractive of a unified theory is more than justified, but does it really need to be the case? Is it possible that the universe works really...

From this video of a Feynman lecture: At 39:30 he (Feynman) draws a line from the eye to the mirror, and then continues the line through the mirror, to represent where the image appears to come from (it appears to come from behind the mirror). Here he is showing the classical way of...

Homework Statement Using my classnotes and what the professor did, it is not clear to me as how I must tackle the following problem. I'm given the potential ##V(x)= V_0 \left ( \frac{x^2}{2} -K \right ) e^{-a x^2}## where a>0. I must estimate via Ritz method the ground state energy. I must use...

Homework Statement In a QM problem I must calculate the expectation value of the kinetic energy, namely ##\langle \Psi _c ,\frac{ \hat { \vec p } ^2}{2m} \Psi _c \rangle##. Where ##\Psi _c=ce^{-\alpha x^2}##. Homework Equations ##\int _{-\infty}^\infty \exp \{ -a x^2 +bx \} dx =...

Any comments (pro-con) on this Quantum Bayesian interpretation of QM by Fuchs & Schack ?: http://arxiv.org/pdf/1301.3274.pdf

Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...

It is often stated that quantum mechanics is able to explain the stability of atoms. I think most explanations are cheating b/c the compare apples and oranges. There are two reasons in classical theory which indicate that atoms should be unstable: A) there is no minimum for the orbit; the...

In QED, Feynman says: "The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate..." I've been frustrated in that I'm still not clear if this is the case (is there still no model to explain the behavior). A similar dynamic seems to...